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Lecture%203%20Annotated

Lecture%203%20Annotated - Life Insurance and Superannuation...

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Life Insurance and Superannuation Models Week 3: Net Premium Valuation March 14, 2011 1 / 21

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Week 3: Net Premium Valuation Summary Contract premiums LI is bought by a life annuity of contract premiums Provide for the benefits, expenses associated with initiating/maintaining contract, profit margins, and deviations due to adverse experience Net premiums Considers only the benefits provided None for allocated expenses, profit or contingency margins Premium principles Principle of equivalence Other premium principles e.g. percentile premiums, exponential premiums References Chapter 6 (Bowers, et al.) or Chapter 5 (Gerber) ACTL3002: Week 3 2
Net Random Future Loss An insurance contract is an agreement between two parties The insurer agrees to pay for insurance benefits; In exchange for insurance premiums to be paid by the insured Denote by PVFB 0 the present value, at time of issue, of future benefits to be paid by the insurer. Denote by PVFP 0 the present value, at time of issue, of future premiums to be paid by the insured. The insurer’s net random future loss is defined by 0 L = L = PVFB 0 - PVFP 0 ACTL3002: Week 3 3

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Principle of equivalence The net premium is the amount of premium required to meet the expected cost of the insurance or annuity benefits under a contract, given mortality and interest rate assumptions. The net premium is determined according to the principle of equivalence by setting E [ L ] = 0 The expected value of the insurer’s net random future loss is equal to zero. This is then equivalent to setting E ( PVFB 0 ) = E ( PVFP 0 ) For example, for a unit of benefit payment, let Z be the PV r.v. associated with the life insurance benefits and Y is the PV r.v. associated with the life annuity premium payments, with π the premium payable annually, then L = Z - π Y so that π = E ( Z ) / E ( Y ) ACTL3002: Week 3 4

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Different Possible Combinations Premium payment Benefit payment annually at the end of the year of death

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Lecture%203%20Annotated - Life Insurance and Superannuation...

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